Problem: The sum of two numbers is $143$, and their difference is $27$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 143}$ ${x-y = 27}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 170 $ $ x = \dfrac{170}{2} $ ${x = 85}$ Now that you know ${x = 85}$ , plug it back into $ {x+y = 143}$ to find $y$ ${(85)}{ + y = 143}$ ${y = 58}$ You can also plug ${x = 85}$ into $ {x-y = 27}$ and get the same answer for $y$ ${(85)}{ - y = 27}$ ${y = 58}$ Therefore, the larger number is $85$, and the smaller number is $58$.